I am wondering if this should read:

New Moon instead of Sabbath in verse 14, as no doubt we have been deceived much greater than these verses alone.
Why else is New Moon a greater Worship Day than the seventh day Sabbath, since more and greater sacrifices were required to be offered on the day of The New Moon, than upon the 7th day Sabbath? (Read Ezekiel 46)

Exodus 31:12
12 And YHVH spake unto Moses, saying,
Exodus 31:13
13 And you speak to the sons of Israel, saying, surely My Sabbaths you shall keep for a sign (owth-226) these between Me and you for your generations; to know that I YHVH your sanctifier.

The New Moon day signals (signs-owth-226) the beginning of a New Month, with her four synchronous weeks.

226 'owth {oth} Hebrew: noun feminine
probably from 225 (in the sense of appearing);

Possible Definitions:
1) sign, signal
1a) a distinguishing mark
1b) banner
1c) remembrance
1d) miraculous sign
1e) omen
1f) warning
2) token, ensign, standard, miracle, proof

Exodus 31:14
14 Ye shall keep the New Moon Day therefore; for it [is] holy unto you: every one that woundeth-(dissolve) it shall surely be put to death: for whosoever doeth work therein, that soul shall be cut off from among his people.

(In the Hebrew here is a double diamond colon- indicating the end of the sentence)

From The Universal Jewish Encyclopedia
[410] Holiday Prayers
... 1. Sabbath and New Moon (Rosh Hodesh), both periodically recurring in the course of a year. The New Moon is still, and the Sabbath originally was, dependent upon the lunar cycle. Both date back to the nomadic period of Israel. Originally the New Moon was celebrated in the same way as the Sabbath; gradually it became less important, while the Sabbath became more and more a day of religion and humanity, of religious meditation and instruction, of peace and delight of the soul, and produced powerful and beneficent effects outside of Judaism.

Before the Scriptures were altared under Roman threat, they kept the New Moon in the same manner as the Sabbath.

That Hillel II changed the Sabbath from the lunar based weeks, to Saturday, and was also forbidden by Rome to Proclaim The Day of The New Moon, He also likely changed not only the fourth command, substituting Sabbath for New Moon there, but likely He changed it also Here in Exodus 31: 13 and 14

Another point, Y'hoshua was commanded to rise up and march around Jericho on The New Moon day.
It is clearly a spiritual worship day, but not necessarily a "rest" day but rather a "pause" day from the normal labor of the six working days, a "set apart" day.

Exodus 31:15
15 Six days may work be done; and on day the seventh [is] a sabbath of rest, holy to YHVH: whosoever doeth [any] work in the sabbath day, he shall surely be put to death.
Exodus 31:16
16 Wherefore the children of Israel shall keep the sabbath, to observe the sabbath throughout their generations, [for] a perpetual covenant.
Exodus 31:17
17 It [is] a sign between Me and the children of Israel for ever: for [in] six days YHVH made heaven and earth, and on the seventh day He rested, and was refreshed.
Exodus 31:18
18 And He gave unto Moses, when He had made an end of communing with him upon mount Sinai, two tables of testimony, tables of stone, written with The Finger of Elohim.

Since Ezekiel 46:1 & 3 tells us that New Moon and Sabbath are both "Worship" times, then maybe both should be kept in the same manner, except the priests erected or took down the tabernacle on the New Moon Day, they were rested after resting on the previous day of the 7th day Sabbath, with possibly an extra interval day between every other moon for the .5 of 29.5 day interval.

For working on the New Moon, the penalty was "cut off" from his people, for "profaning" the new moon was the death penalty.

For working on the 7th day Sabbath was the death penalty.